Minimum Spacing of Thermally Induced Cracks in Brittle Solids

Abstract

When the temperature at the free surface of a linearly elastic brittle half-plane, which is initially uniform throughout the solid, is suddenly reduced by a large amount and then kept constant thereafter, a thermal boundary layer whose thickness increases with time, forms close to the free surface. Because of the consequent thermal contraction, edge cracks may form within the thermal boundary layer. For a system of equally spaced straight-edge cracks, growing collinearly with increasing thickness of the thermal boundary layer, the average minimum crack spacing is estimated on the basis of: (a) energy consideration, (b) stress consideration, and (c) consideration of stability of the growth of interacting cracks. It is shown that for a given temperature profile, one can develop a general stability chart which, in particular, gives a complete growth regime of the interacting cracks (no crack branching is included).